Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Quarti Tractatus
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<
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xml:space
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<
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N26020
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xml:space
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">Si
<
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queſtio eēt vera / ſeq̇retur / vbicū aliqua ponã al
<
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/>
teratīa et ſua reſiſtētia incipiūt a nõ gradu põne et
<
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teſiſtētie vniformiter ↄ̨tinuo augeri ponã alteratiã
<
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/>
cõtinuo velocius creſcēte ſua reſiſtēti: a ip̄a ponã al
<
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/>
teratiã ↄ̨tinuo vniformiter alterabit: ſꝫ ↄ̨ñs eſt fĺm /
<
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igit̄̄ ex quo ſequit̄̄ </
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<
s
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xml:space
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">Seq̄la ꝓbat̄̄ / ſit a. ponã alteratiã
<
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et .c. reſiſtētia q̄ vniformiter incipiãt creſcere a non
<
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/>
gradu ī iſtã a. ponã alteratiã ↄ̨tinuo ī f. ꝓportiõe ve
<
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locius creſcēte ꝙ̄ ip̄a c. reſiſtētia. </
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<
s
xml:id
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N26038
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xml:space
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">Et tūc arguit̄̄ a. po
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nam cõtinuo vniformiter alterare: q2 cõtinuo ſe ha
<
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/>
bebit in f. ꝓportiõe ad c. reſiſtētiã: igit̄̄ cõtinuo alte
<
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/>
rabit ab f. ꝓportiõe: et per ↄ̨ñs cõtinuo vniformiter
<
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</
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<
s
xml:id
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N26042
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xml:space
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">Cõſequētia pꝫ: et probatur añs: q2 quocū inſtanti
<
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dato in toto precedēti tēpore creuit a. ponã in f. ꝓ-
<
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/>
portiõe velocius a nõ gradu ꝙ̄ c. reſiſtētia: igit̄̄ ī illo
<
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/>
tēpore adequate in f. ꝓportione maiorē latitudinē
<
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/>
acq̇ſiuit a non gradu ꝙ̄ c. reſiſtētia: et ꝑ ↄ̨ñs in quoli
<
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/>
bet tĺi inſtanti ipſa a. ponã alteratiã eſt in f. ꝓpor-
<
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tione maior ꝙ̄ ip̄a c. reſiſtētia: et ſic cõtinuo ſe habe
<
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bit in f. proportiõe ad c. reſiſtētiã / quod fuit ꝓbandum
<
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</
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<
s
xml:id
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N26054
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xml:space
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">Iam arguit̄̄ falſitas ↄ̨ñtis: q2 tunc ſequeret̄̄ / vbi-
<
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/>
cū aliqua ponã alteratiã ita alterat vniformiter
<
lb
/>
per ſui vniforme cremētū a nõ gradu ponã etc̈. / vt di
<
lb
/>
ctū eſt: oīs minor ſufficiēs alterare eandē c. reſiſten
<
lb
/>
tiã vniformiter cõtinuo creſcens cū ipſa ponã a. cõ-
<
lb
/>
tinuo intēdit motū ſuū alteratiõis: et oīs maior cõ-
<
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/>
tinuo remittit: ſꝫ ↄ̨ñs videt̄̄ falſuꝫ: igit̄̄ illud ex quo
<
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ſequit̄̄. </
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<
s
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N26065
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xml:space
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">Sequela ꝓbat̄̄ / et ſit b. illa ponã minor ipſa
<
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/>
a. ponã et vniformiter cõtinuo et eque velociter cre-
<
lb
/>
ſcens cū a. et tamē a certo gradu / et arguit̄̄ / ↄ̨tinuo
<
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ꝓportio inter b. põnam et c. reſiſtētiã auget̄̄. </
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>
<
s
xml:id
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N2606E
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xml:space
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preserve
">et ꝑ con
<
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ſequēs cõtinuo b. intēdit motum ſuū alterationis.
<
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/>
</
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<
s
xml:id
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xml:space
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">Cõſequētia pꝫ: et ꝓbatur añs: quia continuo b. ma
<
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/>
iorem ꝓportionē acq̇rit ꝙ̄ c. reſiſtētia: igit̄̄ cõtinuo
<
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/>
proportio inter b. põnã: et c. reſiſtētiam auget̄̄. </
s
>
<
s
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="
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xml:space
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">Ptꝫ
<
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/>
ↄ̨ſequētia ex primo correlario ſecunde cõcluſionis
<
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/>
octaui capitis ſecunde partis: et añs probat̄̄ / q2 cõ
<
lb
/>
tinuo a. acq̇rit tãta ̄ta c. / vt pꝫ ex primo correlario
<
lb
/>
quarte cõcluſionis octaui capitis preallegati. </
s
>
<
s
xml:id
="
N26086
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xml:space
="
preserve
">Nã
<
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inter a. et c. creſcētes cõtinuo manet eadem propor
<
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/>
tio puta f. ꝑ te et b. cõtinuo maiorē proportionem
<
lb
/>
acquirit ꝙ̄ a. / vt patet ex octaua ſuppõne quarti ca
<
lb
/>
pitis ſecūde partis (continuo em̄ tantam latitudi-
<
lb
/>
nē ponē acquirit b. ponã minor ſicut a. maior) / igit̄̄
<
lb
/>
continuo b. maiorē proportionē acquirit ꝙ̄ c. reſi-
<
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/>
ſtētia / qḋ fuit probandū. </
s
>
<
s
xml:id
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xml:space
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">Et eadē ꝓbatiõe ꝓbabis /
<
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oīs ponã alteratiã maior continuo vniformiter et
<
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/>
eque velociter creſcens ſicut a cõtinuo remittit ſuū
<
lb
/>
motū alteratiõis: cū continuo mīorē ꝓportionē ac-
<
lb
/>
quirat ex octaua ſuppõne preallegata ꝙ̄ a. et ꝑ ↄ̨ñs
<
lb
/>
minorē ꝙ̄ c. reſiſtētia: et ſic cõtinuo ꝓportio inter b.
<
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/>
et c. diminuitur: vt pꝫ ex ſecūda parte primi correla
<
lb
/>
rii tertie ↄ̨cluſiõis octaui capitis preallegati.</
s
>
</
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<
p
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<
s
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xml:space
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">Sexto principaliter arguitur ſic </
s
>
<
s
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="
N260AC
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xml:space
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">Si
<
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/>
queſtio eſſet s: ſeq̇retur aliquod alterans ꝑ infini
<
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/>
tam alterationē in determinato tꝑe ꝓducere finitã
<
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/>
qualitatē: ſꝫ ↄ̨ñs eſt falſum: igit̄̄ ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N260B5
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xml:space
="
preserve
">Seq̄
<
lb
/>
la ꝓbatur: et volo / diuidat̄̄ hora ꝑ partes propor
<
lb
/>
tionales ꝓportione dupla: et a. alterans in prima
<
lb
/>
parte proportionali alteret b. paſſuꝫ ꝓducēdo qua
<
lb
/>
litatē aliquãtulū velociter: et in ſecūda in duplo ve
<
lb
/>
lociꝰ et ī tertia ī triplo velociꝰ ꝙ̄ in prima: et ī quar
<
lb
/>
ta in quadruplo velociꝰ ꝙ̄ ī ṗma: et ſic ↄ̨ñter ꝓcedē
<
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/>
do ſeratim ꝑ oēs ſpēs ꝓportiõis mĺtiplicis. </
s
>
<
s
xml:id
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N260C6
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xml:space
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">Quo
<
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poſito ſic argumētor a. alterãs īfinite velociṫ alte-
<
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/>
rat b. paſſū ī illa hora: q2 aliquãtulū velociṫ: et ī du
<
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="
Capi. primum
"/>
plo: et in triplo: et ſic in īfinitū: vt pꝫ ex caſu: et ſolū in
<
lb
/>
illa hora ꝓducit q̈litatē finitã: igit̄̄ aſſumptū verū.
<
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/>
</
s
>
<
s
xml:id
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N260D3
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xml:space
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">Probat̄̄ minor: et pono argumēti gr̄a / a. in ṗma
<
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/>
parte ꝓportionali hore mediãte motu alteratiõis
<
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/>
ꝓducat vnū gradū q̈litatis (loquor de gradibꝰ en-
<
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/>
titatis for̄e ſꝑ ī hoc maṫia et manifeſtū e mediãte
<
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/>
tali motu alteratiõis ꝑ totã horã extenſo ſiue cõti-
<
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nuato a. ꝓducit duos gradus qualitatis: g̊ mediã-
<
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/>
te totali illa velocitate difformi adequate ī illa ho-
<
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/>
ra ꝓducit q̈tuor gradus forme: et ꝑ ↄ̨ñs finitã formã
<
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/>
qualitatis / qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
="
N260E6
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xml:space
="
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">Cõſequētia et deductio
<
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pꝫ ex ſcḋa cõcluſiõe tertii capitis ſcḋi tractatꝰ: et ex
<
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tertio argumēto eiuſdē capitis.
<
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xml:space
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</
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<
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xml:space
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">¶ Dices et bñ ↄ̨cedē
<
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do illatū: nec illud eſt incõueniēs capiēdo ly īfinitū
<
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/>
ſyncathegorematice: et capiēdo ly alterationē ꝓ al
<
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/>
teratiõe ꝑtiali. </
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>
<
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xml:space
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">Nã ly determīato tꝑe ſtat ↄ̨fuſe tm̄
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</
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<
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">Quare aliqḋ alterãs ꝑ infinitã alterationē ꝑ aliqḋ
<
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tp̄s ꝓducit ſolū q̈litatē finitã ̄uis ꝑ nullū tp̄s ꝑ in
<
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/>
finita alteratiõeꝫ ꝓducat q̈litatē ſolū finitã. </
s
>
<
s
xml:id
="
N26106
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xml:space
="
preserve
">In ꝓpo
<
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/>
ſito eī tota illa velocitas alteratiõis ē finita corrñ
<
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des velocitati / q̄ eſt ī ſcḋa ꝑte ꝓportionali tꝑis / vt ſu
<
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/>
pra dictū ē de velocitate motꝰ localis q̊ ad effectum
<
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/>
loco p̄allegato. </
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>
<
s
xml:id
="
N26111
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xml:space
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">Sꝫ ↄ̈ / q2 tunc ſeq̄ret̄̄ / ſi aliqḋ alte-
<
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/>
rans alteraret aliqḋ paſſuꝫ aliquãtula velocitate ī
<
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/>
prīa ꝑte ꝓportionali hore diuiſe ꝑ partes ꝓportio
<
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/>
nales ꝓportiõe ſexq̇tertia: et in ſcḋa ꝑte ꝓportiona
<
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/>
li alteraret in ſexq̇altero velocius: et in tertia ī ſexq̇
<
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/>
altero velociꝰ ꝙ̄ in ſcḋa: et ſic ↄ̨ñter in q̈libet ſequēti
<
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/>
in ſexq̇altero velocius ꝙ̄ in īmediate p̄cedēti: tūc il-
<
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/>
lud alterãs ſolū finite velociter alteraret ī tota illa
<
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/>
hora: finitã qualitatē adequate ī illa hora ꝓduce
<
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/>
ret: ſꝫ ↄ̨ñs eſt falſuꝫ: igit̄̄ illud ex q̊ ſequit̄̄. </
s
>
<
s
xml:id
="
N26126
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xml:space
="
preserve
">Seq̄la ꝓ-
<
lb
/>
batur: q2 ſi hora eēt diuiſa ꝑ partes ꝓportionales
<
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/>
ꝓportiõe dupla: et illud alterãs alteraret in q̈libet
<
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/>
parte ꝓportionali ſeq̄nti in ſexq̇altero velociꝰ ꝙ̄ in
<
lb
/>
īmediate p̄cedēti: tūc tota illa velocitas alteratõis
<
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/>
adequate eſſet finita et finita qualitas mediãte ta-
<
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/>
li alteratione in illa hora adeq̈te ꝓduceret̄̄ / vt patꝫ
<
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ex ſeptīa ↄ̨cluſiõe tertii capitis .2. tractatꝰ. </
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>
<
s
xml:id
="
N26137
"
xml:space
="
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">igit̄̄ ī ca
<
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/>
ſu propoſito pari rõe finita qualilas adequate ꝓ-
<
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/>
ducit̄̄ mediãte illa totali alteratiõe in hora adeq̈te
<
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/>
</
s
>
<
s
xml:id
="
N2613F
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xml:space
="
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">Sꝫ falſitas ↄ̨ñtis facile oñdit̄̄ ex ſexta cõcluſione .3.
<
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capitis preallegati. </
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>
<
s
xml:id
="
N26144
"
xml:space
="
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">hoc addito / qualitas ꝓducta
<
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/>
in propoſito eſt ibi ſpacium pertranſitum. </
s
>
<
s
xml:id
="
N26149
"
xml:space
="
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">¶ Huic
<
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propoſito poteris applicare ſecūdū: tertiū: et quar
<
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/>
tum argumeutū tertii capitis ſecūdi tractatꝰ. </
s
>
<
s
xml:id
="
N26150
"
xml:space
="
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">Ap-
<
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/>
plica etiã imaginationē ordinū partiū proportio
<
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/>
naliū iuxta doctrinam prime et ſecūde cõcluſionem
<
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/>
ſeptimi capitis prime partis.</
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>
</
p
>
<
p
xml:id
="
N26163
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<
s
xml:id
="
N26164
"
xml:space
="
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">Septimo principaliter arguitur ſic.
<
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/>
</
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>
<
s
xml:id
="
N26168
"
xml:space
="
preserve
">q2 ſi queſtio eēt a: ſeq̇retur / qḋlibet alterãs ali-
<
lb
/>
quã reſiſtētiã a maiori proportiõe velocius altera-
<
lb
/>
ret q̊libet alterãte eãdē reſiſtētiã a minori propor-
<
lb
/>
tiõe: ſꝫ ↄ̨ñs eſt falſam: igit̄̄ illud ex q̊ ſeq̇tur. </
s
>
<
s
xml:id
="
N26171
"
xml:space
="
preserve
">Seq̄la
<
lb
/>
patꝫ: et falſitas ↄ̨ñtis arguit̄̄: q2 qḋlibet alterãs ali
<
lb
/>
quã reſiſtētiã a certa ꝓportiõe difficiliꝰ agit q̊libet
<
lb
/>
alterãte eãdem reſtētiã a mīori ꝓportiõe: igit̄̄ qḋlꝫ
<
lb
/>
alterans aliquã quolibet alterãte eandē reſiſtentiã
<
lb
/>
a minori proportiõe. </
s
>
<
s
xml:id
="
N2617E
"
xml:space
="
preserve
">Patꝫ hec ↄ̨ña: q2 omīs pona
<
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/>
difficilius agens ſiue ꝓducēs aliquid tardius il-
<
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/>
lud agit ſiue producit. </
s
>
<
s
xml:id
="
N26185
"
xml:space
="
preserve
">Et probatur añs: et ſit a. po-
<
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/>
nã alterãs c. reſiſtentiã ab f. proportiõe: et b. pona
<
lb
/>
alterans eandē c. reſiſtentiã ab .h. proportione mi-
<
lb
/>
nori: et arguitur / a. difficilius agit ſiue alterat c.
<
lb
/>
reſiſtētiã ꝙ̄ b: q2 difficultas actõis ip̄ius a. ē maior
<
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/>
̄ difficultas actõis ipſiꝰ b. / igr̄ a. difficiliꝰ agit ꝙ̄ b.
<
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/>
</
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>
<
s
xml:id
="
N26193
"
xml:space
="
preserve
"/>
</
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>
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>
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